# Thread: Choosing K out of N Objects Formula Question

1. ## Choosing K out of N Objects Formula Question

I'm having trouble interpreting the formula that is "with regard to order" and "without replacement". How exactly would I compute the upper right hand formula with, for example, k=5 and n=10?

Sorry for the elementary question and thanks for your time.

2. ## Re: Choosing K out of N Objects Formula Question

Originally Posted by divinelogos
I'm having trouble interpreting the formula that is "with regard to order" and "without replacement". How exactly would I compute the upper right hand formula with, for example, k=5 and n=10?
You really should learn to post in LaTeX. It hard to know exactly what you are asking.
$\displaystyle \begin{array}{*{20}{c}} {{n^k}}&{n(n - 1) \cdots (n - k + 1)} \\ {\binom{n-1+k}{k}}&{\binom{n}{k}} \end{array}$
If so the "upper right hand formula" is the permutation of $\displaystyle N$ choosing $\displaystyle k$.
i.e. $\displaystyle _N\mathcal{P}_k=\frac{N!}{(N-k)!}$.